Rodgers capitalised on a flick on by Lee Hughes to blast home right at the death just as a goalless draw looked on the cards.
It was no less than the hosts deserved after a blistering start. Hughes spurned an opportunity after just 46 seconds, before Rodgers clipped the post and Hughes hit the crossbar from John Thompson’s cross.
The Millers gave the hosts a scare just after the restart with Marcus Marshall beating Kasper Schmeichel only for the goal to be ruled out for offside.
County saw Ben Davies fire wide and Hughes had a header cleared off the line by Ian Sharps, before Rodgers stole the headlines.
Sharps came close at the other end late on, but headed straight at Schmeichel as County clung on to go 10 games unbeaten.